2005_Solutions_Grades 5-6-2005_Solutions_Levels

2005_Solutions_Levels_5&6
Pdf Summary
The Math Kangaroo 2005 competition provides a set of math questions for students to solve, with solutions that demonstrate various problem-solving techniques. Below is a brief summary of some solutions provided:<br /><br />1. **Butterfly Problem (Solution: E)**: Calculating the remaining distance after subtractions gives 1290.<br /><br />2. **Candy Distribution (Solution: C)**: Determines that Olla has 6 pieces of candy when Anna gets an equal share.<br /><br />3. **Kangaroo Arrangement (Solution: B)**: Reorganizing kangaroos gives one in each necessary row and column.<br /><br />4. **Animal and Leg Count (Solution: D)**: Summing legs from animals and people totals 24.<br /><br />5. **Arithmetic Manipulation (Solution: D)**: Breaking down and combining moves results in the number 202505.<br /><br />6. **Ant's Path (Solution: D)**: The calculated ant path totals 60 cm.<br /><br />7. **Marble Colors (Solution: D)**: Determining non-white marbles leaves 7 brown marbles.<br /><br />8. **Card Moves (Solution: A)**: Switching positions in two moves arranges cards correctly.<br /><br />9. **Multiples of Three (Solution: E)**: Identifies 103 as not derived from multiplying three.<br /><br />10. **Time Calculation (Solution: C)**: A breakdown of an hour calculated from a day fraction.<br /><br />11. **Napkin Cuts (Solution: C)**: Systematic cutting results in 37 pieces.<br /><br />12. **Mowgli's Travel Time (Solution: D)**: Total foot travel calculated at 48 minutes.<br /><br />13. **Garden Area (Solution: C)**: Rectangular area is calculated to 8 m².<br /><br />14. **Peanut Distribution (Solution: E)**: 7 members get more than grandpa's distribution.<br /><br />15. **Odd Digit Numbers (Solution: B)**: Combinatorial counting results in 20 possible combinations.<br /><br />16. **Cube Configuration (Solution: B)**: Consistent characteristics identify a particular option.<br /><br />17. **Middle Number Formula (Solution: B)**: 403 as the largest of five numbers.<br /><br />18. **Divisors of 100 (Solution: E)**: Lists 9 unique divisors.<br /><br />19. **Frame Width (Solution: C)**: Calculated using the perimeter difference, yielding 1 decimeter width.<br /><br />20. **Shape Puzzle (Solution: E)**: There are 10 triangles, 3 more than squares.<br /><br />21. **Chest Unlocking (Solution: E)**: 8 lock openings yield 50 coins.<br /><br />22. **Sequential Operations (Solution: D)**: Summation to arrive at 82.<br /><br />23. **Number Multiples (Solution: D)**: Finding consistent conditions where a number is a multiple of six.<br /><br />24. **Paint Consumption (Solution: D)**: Unpainted cubes require 0.5 gallons more paint.<br /><br />25. **Area Ratios (Solution: D)**: Ratio of shaded versus unshaded parts is 2:3.<br /><br />26. **Watch Note Validity (Solution: C)**: 18 hours where the note applies.<br /><br />27. **Prism Dimensions (Solution: D)**: Data shows height must be 3 cm.<br /><br />28. **Perfect Square Options (Solution: D)**: Logical deduction of possible digit setups results in 421, 463, 931, 962.<br /><br />29. **Shaded Triangular Area (Solution: B)**: Shaded region calculates to an equivalent of 22.5 triangle areas.<br /><br />30. **Seating Arrangement (Solution: D)**: Deduction leads to Ella sitting farthest to the right.<br /><br />This compilation showcases an array of problem-solving skills necessary for a math competition setup. Each question requires analytical and deductive reasoning across various mathematical topics.
Keywords
Math Kangaroo 2005
math competition
problem-solving techniques
math questions
solutions
analytical reasoning
deductive reasoning
mathematical topics
student competition
math skills